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Statistical signal processing [1] traditionally focuses on extraction of information from noisy measurements. Typically, parameters or states are estimated by various filtering operations. Here, the quality of signal processing operations will be assessed by evaluating the statistical uncertainty of the result [2]. The processing could for instance simulate, correct, modulate, evaluate, or control the response of a physical system. Depending on the addressed task and the system, this can often be formulated in terms of a differential or difference signal processing model equation in time, with uncertain parameters and driven by an exciting input signal corrupted by noise. The quantity of primary interest may not be the output signal but can be extracted from it. If this uncertain dynamic model is linear-in-response it can be translated into a linear digital filter for highly efficient and standardized evaluation [3]. A statistical model of the parameters describing to which degree the dynamic model is known and accurate will be assumed given, instead of being the target of investigation as in system identification [4]. Model uncertainty (of parameters) is then propagated to model-ing uncertainty (of the result). The two are to be clearly distinguished – the former relate to the input while the latter relate to the output of the model.

Deterministic Sampling for Quantification of Modeling Uncertainty of Signals